Airfoil and a turbine apparatus

ABSTRACT

The present invention provides a turbine airfoil for relative movement in an ambient fluid, and a turbine apparatus comprising at least one airfoil. The airfoil comprises a main spar having two hill formations and discharge means operable to discharge evaporative and condensing fluids outwardly into the ambient fluid flowing over the main spar. The first of these hill formations accelerates the flow of the ambient fluid until it reaches the speed of sound. After the first hill formation the Mach number continues to increase and the evaporative fluid is discharged into the ambient causing the air to cool which accelerates the ambient flow further and decreases the pressure. On the second hill formation the lower pressure causes a thrust. As the flow moves relative to the second hill formation the Mach number decreases and then increases as it descends the second region. A condensing fluid is discharged causing the water content of the air to condense releasing heat which results in a decrease in Mach number and an increase in pressure. The increased pressure on the second hill formation will produce a thrust which can be used to turn a rotor. The present invention provides an airfoil for producing work and power directly from the moisture in the air. It has no dependence on wind speed and its energy source is directly derived from the always available ambient atmosphere.

The present invention relates to an airfoil for relative movement in anambient fluid and to a turbine apparatus having an airfoil.

Apart from nuclear and tidal processes all energy on the earth can bedescribed as deriving from the sun itself, whether directly or storedover considerable time periods. When the sun shines on the planet, theenergy provokes many processes—climatic effects being the most obvious,and it is well known that life, both plant and animal is sustained bythis source. Whilst the majority of the suns energy is used to heat thevast system surrounding the sun, a large proportion of the sun's energyresults in evaporation of water, such as from major water bodies. Thisevaporation provides rainfall and maintains a vast amount of watervapour, a small proportion of which may accumulate to form condensingclouds. Conventional power sources are derived from chlorophilic andother organic processes, which use less than 1% of the suns energy.

Renewable energy windmills are known to take advantage of evaporationand condensation processes to generate work and power. The most recentdevelopments are the Barton preheated expansion engine and the EOLA windturbine. These machines are used to supply energy (Barton made) andwater (EOLA turbine) in limited circumstances. The Barton enginerequires pre heated dried air and evaporating water to extra low gradeenergy efficiency and is restricted to turbine exhausts or preheated dryair such as solar arrays. The EOLA is a conventional air turbineattached to a conventional air conditioning unit.

The known devices rely on intermittent wind speed and/or a secondaryenergy source, such as solar power, for producing power, which demands astandby conventional power generator. It is an object of the presentinvention to provide an airfoil and a turbine apparatus which goes atleast some way toward overcoming the above problems and/or which willprovide the public and/or industry with a useful alternative.

Further aspects of the present invention will become apparent form theensuing description which is given by way of example only.

According to the invention, there is provided a turbine airfoil forrelative movement in an ambient fluid, comprising:

-   -   a main spar having a cross-sectional shape of an airfoil with a        top side wall and a bottom side wall, a leading edge, a trailing        edge, and a camber line extending from the leading edge to the        trailing edge, the movement of the airfoil relative to the        ambient fluid such that the ambient fluid flows over the main        spar in a downstream direction from the leading edge to the        trailing edge, and    -   discharge means operable to discharge fluid outwardly into the        ambient fluid flowing over the main spar;    -   characterised in that a side wall of the main spar comprises        sequentially from the leading edge to the trailing edge a first        hill formation and a second hill formation, each hill formation        comprising a first region of progressively increasing distance        from the camber line, a second region of progressively        decreasing distance from the camber line, and a crest at an        interface between the first and second regions,    -   whereby, the first region of the first hill formation is        operable to interact with the ambient fluid to accelerate it        from a high subsonic relative speed to a sonic relative speed        over the crest of the first hill formation and supersonic speed        after the crest of the first hill formation;    -   the discharge means discharges an evaporative fluid to evaporate        into the ambient fluid before condensation onset in the second        region of the first hill formation, said second region of the        first hill formation interacts with the ambient fluid to        accelerate the ambient fluid from supersonic relative speed to        higher supersonic relative speed;    -   the first region of the second hill formation is operable to        interact with the ambient fluid to decelerate and maintain the        ambient fluid at supersonic relative speed over the crest of the        second hill formation, and    -   the discharge means is further operable to discharge a        condensing fluid to capture or nucleate condensation shock in        the ambient fluid flowing over the second region of the second        hill formation which decelerate the ambient fluid from        supersonic relative speed to subsonic relative speed and        generate a pressure on the side wall and thereby impart thrust        on the air foil.

The present invention provides an airfoil for producing work and powerdirectly from the moisture in the air. It has no dependence on windspeed and its energy source is directly derived from the alwaysavailable ambient atmosphere. Furthermore, the condensed moisture is abountiful water source and in use, allows for refrigeration, airconditioning and cryogenic superconducting. Finally, the residual heatcan be used for immediate local requirements.

The characteristic design of the airfoil provides two hill formationsmounted along its length. The first of these hill formations acceleratesthe flow of the ambient fluid until it reaches the speed of sound. Afterthe first hill formation the Mach number continues to increasesupersonically as the area increases. The evaporative fluid, such as aspray of water droplets, is discharged into the ambient either along thedescent or at the bottom of the first hill formation. These evaporatecausing the air to cool. This in turn accelerates the ambient flowfurther and decreases the pressure. On the second hill formation thelower pressure causes a thrust. As the flow moves relative to the secondhill formation the Mach number decreases along the first region and thenincreases as it descends along the second region. At a point along thissecond hill formation the Mach number reaches the condensation Machnumber. At or before this point, a condensing fluid is dischargedcausing the water content of the air to condense releasing heat. Thiswill cause a decrease in Mach number and an increase in pressure. Theincreased pressure on the second region of the second hill will producea thrust which can be used to turn a rotor.

The present invention is concerned with an airfoil and turbine apparatusthat is operable to control condensation and evaporation of ambient airto allow the heat released to be harnessed to produce work. The presentinvention is therefore not restricted by the above limitations of theprior art and provides a primary renewable energy and water capturingdevice.

In another embodiment of the invention, the evaporating fluid isdischarged before an incipient condensation shockpreventing/compensating for it in the ambient fluid flowing over thefirst hill formation

In another embodiment of the invention, the condensing fluid isdischarged before condensation shock occurs in the ambient fluid flowingover the second hill formation.

In another embodiment of the invention, the discharge means comprises atleast one nozzle, and the evaporative fluid and condensing fluid isconveyed from a supply to the or each nozzle via an arrangement ofconduits in the airfoil. Variable pinhole size for the nozzle or nozzleswill allow variable flow rate and droplet size of the discharged fluid.

In another embodiment of the invention, the main spar comprises a hollowcavity containing a working fluid, whereby the cavity is divided into aplurality of interconnected chambers.

In another embodiment of the invention, each chamber comprises valvemeans operable to control the flow of the working fluid between thechambers to adjust the pressure and/or temperature of the working fluidin each chamber independently.

In another embodiment of the invention, the evaporative fluid is one ora combination of: water, liquid nitrogen and a hydrocarbon, such asmethanol.

In another embodiment of the invention, the evaporative fluid comprisesfluid particles that have a diameter operable to evaporate in the scaleof the turbines designed size. To allow for this and other ambientenvironmental factors the droplet size can be varied by variable outletsize, variable flow rates and variable pressure and temperature. Theseconditions are determined by the ducting, chambers and variable nozzlesizes. The spinning head centrifugal force or outside pumping managesthese conditions using causing the compression of gases and/or heatexchange with the outside atmosphere for temperature management.

In another embodiment of the invention, the condensing fluid comprisesfluid particles that are cooled, statically charged, such as droplets ofwater, brine and ice particles.

In another embodiment of the invention, the ambient fluid is moist air.

In a further aspect of the invention there is provided a turbineapparatus having at least one airfoil as claimed in any one of thepreceding claims, the apparatus comprising:

-   -   a turbine shaft and at least one rotor extending axially from        the shaft, whereby an airfoil is carried at the tip of each        rotor,    -   an arrangement of conduits within the shaft and each rotor        through which the evaporative and condensing fluids are supplied        to the airfoil,    -   each rotor is configured to interact with the ambient fluid to        rotate such that the leading edge of an airfoil moves through        the ambient fluid to thereby rotate the turbine shaft.

The turbine apparatus of the present invention taps into the energyreserve created by evaporation and condensation processes to provideenergy that can be converted into electricity or other usable energyforms. By doing so, the turbine apparatus will generate power from theatmosphere using the water content of the air as its energy source. Whenoperated in a dry climate, the condensed water produced as an output maybe captured and used for irrigation purposes.

The present invention thus produces work and power directly from themoisture in the air. It has no dependence on wind speed and its energysource is directly derived from the always available ambient atmosphere.The condensed moisture is a bountiful water source, and a cold coreallows for refrigeration, air conditioning and cryogenicsuperconducting. Any residual heat can be used for immediate localrequirements.

In another embodiment of the invention, the induced condensation shockis operable to condense fluid particles in the ambient fluid and theairfoil can be configured to deflect the condensed fluid into at leastone collection means of the apparatus.

In another embodiment of the invention, the collection means comprisesone or more of:

-   -   channels formed in a ducting through which condensed fluid        content flows into a collection chamber;    -   a collection surface of a housing, netting or other surface        surrounding the turbine against which condensed fluid content is        deflected into a collection chamber; and    -   one or more cyclone or vortex tubes and a collection chamber to        collect condensed fluid content along the turbine shaft.

In another embodiment of the invention, the turbine further comprisesenergy conversion means to convert energy generated by the rotatingturbine shaft into electrical and/or mechanical energy.

In another embodiment of the invention, the energy conversion means isprovided in a housing of the turbine apparatus, and the shaft is coupledto the housing, whereby conducting windings of the energy conversionmeans for generating electrical energy are provided in the housing.

The present invention provides an engine capable of producing powercomprising of transonic airfoils or bodies of rotation that optionallyinclude rotors and an axial hub. The airfoils or bodies of rotation havea supersonic pocket next to a reducing cross section and at or beforethe minimum cross section, and in which an evaporative spray or coolantgas is introduced through a nozzle. This is tailored to reduce thepressure on the subsequent increasing cross section. At or near themaximum cross section a further spray may be introduced to nucleatesubsequent condensation. After the maximum cross section the reducingcross section causes condensation shock. Liquid spray previouslyintroduced provides nuclei to capture these ephemeral droplets. Theseliquids—typically water- or gases can be carried from the hub to theairfoils or bodies of rotation by the rotors with suitable interiorducting. The condensation shock terminates the supersonic pocket andreturns the airflow to subsonic pressurising the back of the device.

The engine can be used to produce power, to extract axial work from thehub, to sustain the rotation of the rotors, to extract the condensedwater, to avail of the very cold conditions at the tips for cryogenicand superconducting purposes or avail of the centrifugal pumping of thespinning device.

DETAILED DESCRIPTION OF THE INVENTION

The invention will be more clearly understood from the followingdescription of some embodiments thereof, given by way of example only,with reference to the accompanying drawings, in which:

FIG. 1 is a perspective view of an airfoil according to the invention;

FIG. 2 is an end view of the airfoil of FIG. 1;

FIG. 2a is a diagrammatic of the body of rotation of the airfoil ofFIGS. 1 and 2;

FIG. 3 is a diagrammatic side view of the airfoil of FIG. 1;

FIG. 4 is a perspective view of a turbine comprising the airfoilaccording to FIGS. 1 to 3;

FIG. 5 is a detailed perspective view of a cutaway portion of theturbine of FIG. 4;

FIG. 6 is a perspective view of a water collection device embodying theturbine of FIG. 3;

FIGS. 7a to 7c are perspective views showing water flow in the turbineapparatus of FIG. 3;

FIG. 8 is a graph showing contours of Mach number in a stable scenariowith supersonic flow throughout a central section of the airfoil;

FIG. 9 is a graph showing contours of Mach number in an unstablescenario with subsonic flow through a central section of the airfoil;

FIG. 10 is a graph showing pressure variation through a nozzle fordifferent exit pressures;

FIG. 11 is a schematic showing a geometric design for the airfoil usedin the turbine of FIG. 3;

FIG. 12 is a table showing the post-condensation Mach number withvarying temperature and humidity for 10K of cooling;

FIG. 13 is a table of the dip depth with varying temperature andhumidity for 10K of cooling;

FIG. 14 is a table showing the input parameters for a thrust calculationfor the turbine apparatus;

FIG. 15 is a graph showing the contours of Mach number beforeevaporation, is initiated;

FIG. 16 is a graph showing the contours of Mach number afterevaporation, showing the region where evaporation occurs;

FIG. 17 is a graph showing the contours of Mach number aftercondensation, showing the region where condensation occurs;

FIG. 18 is a graph showing the contours of Mach number after exitpressure is raised to atmospheric showing a shockwave after thecondensation, and

FIG. 19 is a graph showing the work cycle for the Brayton cycle.

Referring to the drawings, and initially to FIGS. 1 and 2, there isshown a turbine airfoil, indicated generally by the reference numeral 1,for relative movement in an ambient fluid, such as moist air. Theairfoil 1 comprises a main spar 2 having a cross-sectional shape of anairfoil with a top side wall, indicated generally by the referencenumeral 3, and a bottom side wall, indicated generally by the referencenumeral 4, a leading edge 5, and a trailing edge 6. A camber line 7extends from the leading edge 5 to the trailing edge 6. As the airfoil 1moves relative to or through the ambient fluid in the direction of arrow‘A’ (FIG. 1) the ambient fluid flows over the main spar 2 in adownstream direction from the leading edge 5 to the trailing edge 6.

FIG. 2 is a sectional view of the airfoil, and FIG. 2a shows the body ofrotation of the airfoil of FIG. 2, which in the instance shown gives anexpanding and tapering cylindrical shape and is one example of anairfoil shape embodying the general design principles of the presentinvention. Cylindrical contours may also be applied to the tips 5, 6 ofthe airfoil as required or as desired, such as if a housing is notemployed to manage tip end vortices.

The main spar 2 comprises sequentially from the leading edge 5 to thetrailing edge 6 a first hill formation 8 and a second hill formation 9.Each hill formation 8, 9 comprising a first region 8 a, 9 a ofprogressively increasing distance from the camber line 6, a secondregion 8 b, 9 b of progressively decreasing distance from the camberline, and a crest 8 c, 9 c at an interface between the first regions 8a, 9 a and second regions 8 b, 9 b. Although hill formations are shownin FIGS. 1 and 2 on both the top side wall 3 and the bottom side wall 4,it will be appreciated that hill formations may be located on the topand/or the bottom side wall of the airfoil as required or desired.Reference in the following description will be made to the hillformations being provided on the top side wall 3 only, however thisshould not be seen as limiting.

The main spar 2 comprises a hollow cavity containing a working fluid,whereby the cavity is divided into a plurality of interconnectedchambers. Between the chambers is valve means operable to control theflow of the working fluid between the chambers so that the pressureand/or temperature of the working fluid in each chamber may be adjustedindependently.

As shown in FIG. 3, the airfoil 1 further comprises discharge means,indicated generally by the reference numeral 10 operable to discharge anevaporative fluid 12 or a condensing fluid 13 from the main spar 2outwardly into the moist air flowing over the main spar 2. The dischargemeans comprises at least one nozzle (not shown) and the fluid dischargedfrom the airfoil 1 is conveyed from a supply to each nozzle via aconduit or arrangement of conduits 11 within or arranged along the mainspar 2 of the airfoil 1.

The evaporative fluid 12 is one or a combination of: water, liquidnitrogen and a hydrocarbon, such as methanol, and comprises fluidparticles that have a diameter operable to evaporate according to thesize and scale of a turbine using the airfoil. To allow for this andother ambient environmental factors the droplet size can be varied byvariable outlet size, variable flow rates and variable pressure andtemperature.

The condensing fluid 13 comprises fluid particles that are cooled andstatically charged. Examples of suitable condensing fluids includedroplets of water, brine or ice particles.

When the airfoil is moving relative to an ambient fluid the first region8 a of the first hill formation 8 is operable to interact with theambient fluid to accelerate the ambient fluid from a high subsonicrelative speed to a sonic relative speed over the crest 8 c of the firsthill formation 8.

The discharge means 10 then discharges the evaporative fluid 12 toevaporate into the ambient fluid before condensation onset in the secondregion 8 b of the first hill formation 8 such that the second region 8 bof the first hill formation 8 interacts with the ambient fluid toaccelerate the ambient fluid from low supersonic relative speed to highsupersonic relative speed. The evaporative spray is thus dischargedbefore an incipient condensation shock occurs in the ambient fluidflowing over the first hill formation 8.

The first region 9 a of the second hill formation 9 is operable tointeract with the ambient fluid to decelerate and maintain the ambientfluid at supersonic relative speed over the crest 9 c of the second hillformation 9, and the discharge means 10 is further operable to dischargethe condensing fluid 13 to capture or nucleate condensation shock in theambient fluid flowing over the second region 9 b of the second hillformation 9. The condensing fluid or spray is thus discharged beforecondensation shock occurs in the ambient fluid flowing over the secondhill formation 9. This has the effect of decelerating the ambient fluidfrom supersonic relative speed to subsonic relative speed which in turngenerates pressure on the main spar 2 and thereby imparts a thrust onthe air foil 1.

With reference to FIGS. 4 and 5, and using the same reference numeralsused in FIGS. 1 to 3, shown is a turbine apparatus, indicated generallyby the reference numeral 20, comprising at least one airfoil 1configured according to FIGS. 1 to 3.

The apparatus 20 comprises a turbine shaft 21 and at least one rotor 22extending axially from the shaft 21, whereby an airfoil 1 of FIGS. 1 to3 is carried at the tip or end, indicated generally by the referencenumeral 23, of each rotor 22. Also provided is an arrangement ofconduits within the shaft 21 and each rotor 22 through which theevaporative and condensing fluids are supplied to the conduits 11 of theairfoil 1.

In use the turbine apparatus 20 is configured such that each rotor 22interacts with the ambient fluid to rotate such that the leading edge 5of each airfoil 1 moves through the ambient fluid to thereby rotate theturbine shaft 21.

In operation, as the airfoil 1 moves relative to the ambient fluid theinduced condensation shock at or adjacent the second hill formation 9 isoperable to condense fluid particles in the ambient fluid and theairfoil 1 is configured to deflect the condensed fluid into at least onecollection means of the turbine apparatus 20. In one embodiment, one ormore cyclone or vortex tubes and a collection chamber may be provided tocollect condensed fluid content along the turbine shaft 21. In analternative embodiment, the collection means comprises channels formedin a ducting 24 through which condensed fluid content flows into acollection chamber.

FIG. 6 shows a water collection device 30, comprising the turbineapparatus 20 of FIGS. 4 and 5, and embodying a further water collectionmeans. The water collection device 30 is operable to create a cylinderof rotating air blowing out from the centre of the device or in towardsthe centre. The water collection device 30 comprises a venturi tube 31at both ends of the shaft 21, a set of stators 32 before the throat ofeach venture tube 31 operable to induce rotation in the high speed lowpressure fluid droplet airflow entering the stators 32. A collectionring of pinholes 33 is provided along the ducting 24 and are backed by alow pressure chamber 34 which drains to a collection tank 35. A furtherset of stators 36 are provided after the throat and pinholes 33 whichare operable to reduce rotation and recover airflow energy and pressure.The collection tank 35 surrounds the out-going airflow which containsdroplets of water, and the surface of the tank 35 is operable to collectimpinging droplets which collect in the tank 35.

The turbine apparatus 20 also comprises energy conversion means toconvert energy generated by the rotating turbine shaft 21 intoelectrical and/or mechanical energy. Optionally, the energy conversionmeans is provided in a housing of the turbine apparatus 20, and theshaft 21 is coupled to the housing, whereby conducting windings of theenergy conversion means for generating electrical energy are provided inthe housing.

The work cycle for the present invention will be described withreference to FIG. 19, which shows the work cycle for the Brayton cycle,of which the turbine apparatus of the present invention uses avariation. The turbine apparatus of the present invention seeks toreduce the lowest temperature (3-4). Normally this is restricted by therejection temperature being the ambient air. In this machine therejection temperature can be as much as minus 60 or 70 degreescentigrade. The static temperature reduction (3-4) is aerodynamic causedby isentropic increase in velocity. The rejection heat (4-1) is affectedby evaporation. Temperature increase (1-2) is aerodynamic caused by nearisentropic decrease in velocity. Heat added (2-3) is provided bycondensation or burning hydrocarbons. Note the balance betweenevaporation and condensation is well illustrated and can be calculatedwith this cycle. In reality the flow of evaporation is the easiest tocontrol to balance the condensation. This means the quantity of flow andthe size of the droplets will need to be managed by a valve and variablepinhole arrangement.

The proposed turbine system is a rotor mounted on a vertical axis. Theactual turbines are located at the tips of the rotors and the deviceoperates in a similar principle to a tip jet such as the Fairey Rotodynehelicopter. The propulsion from the turbine creates a thrust whichpushes the rotor in a circle. Unlike helicopters, the objective is notto use the motion to generate a lift force, but rather to generateelectrical power.

In the ducted design, shown in FIGS. 4 to 6, the transonic tips aremounted within a suspended duct. Water spray is channeled up the centralshaft and down the rotors to the tips where it is added to the air. Airis pulled down through the device and removes the water spray from thedevice, as shown in FIG. 7.

Supersonic flow occurs when a fluid starts to move at a velocity greaterthan its wave speed. The most obvious application of this type of flowis in the design of military aircraft which are routinely required to‘break’ the sound barrier. As the fluid is moving faster than it's wavespeed information cannot be passed upstream about potential obstacles.As a result supersonic flow is significantly different from subsonicflows which are more common in everyday scenarios.

The main governing equations in the supersonic regime are the isentropicflow equations. These equations relate the pressure, temperature,density and area changes observed to the Mach number of the flow.

These equations are:

$\begin{matrix}{{{Mach}\mspace{14mu}{Number}\text{:}\mspace{14mu} M} = \frac{V}{\sqrt{\gamma\;{RT}}}} & {{Equation}\mspace{14mu} 1} \\{{{Pressure}\text{:}\mspace{14mu}\frac{p}{p_{0}}} = \left( {1 + {\frac{\gamma - 1}{2}M^{2}}} \right)^{\frac{- \gamma}{\gamma - 1}}} & {{Equation}\mspace{14mu} 2} \\{{{Temperature}\text{:}\mspace{14mu}\frac{T}{T_{0}}} = \left( {1 + {\frac{\gamma - 1}{2}M^{2}}} \right)^{- 1}} & {{Equation}\mspace{14mu} 3} \\{{{Area}\text{:}\mspace{14mu}\frac{A}{A^{*}}} = {\left( \frac{\gamma + 1}{2} \right)^{- {(\frac{\gamma + 1}{2{({\gamma - 1})}})}} \times \frac{\left( {1 + {\frac{\gamma - 1}{2}M^{2}}} \right)^{(\frac{\gamma + 1}{2{({\gamma - 1})}})}}{M}}} & {{Equation}\mspace{14mu} 4}\end{matrix}$SymbolsM=Mach number, V=Velocity, R=Gas Constant, T=Temperature, P=PressureA=Area, y=Ratio of Specific Heats, ρ=Density, φ=Relative Humidity,Y=Throat X=Longitudinal DistanceSubscripts/Superscripts0=Stagnation Property, *=Choked Property

These equations show that as the Mach number of a flow increases thestatic pressures and temperatures will drop. The stagnation propertieswill remain the same so long as there is no heat transfer. The area willalso see an increase as the Mach number increases away from unity in thesupersonic regime, but will also see an increase as it moves from unityin the subsonic regime as well.

The process of condensation in the atmosphere is dependent on thetemperature of the air and the vapour content. For any giventemperature, the air pressure can be calculated fromP=ρRT  Equation 5where p is the density, R is the gas constant of air and T is thetemperature in Kelvin.

Air consists of a certain amount of water vapour and one of theimportant terms for condensation is partial pressure of this vapour. Thepartial pressure is the air pressure multiplied by the relativehumidity. The other important term is the saturation pressure. This isthe pressure at which water will condense and can be determined from theequationP=133.322e ^((20.386-5132/T))

If the partial pressure is greater than the saturation pressure willstart to condense. Similarly, if the partial pressure is less than thesaturation pressure the water will evaporate.

The effects of heating on supersonic flow are complicated because theMach number, temperature and pressure are all interdependent. Onesimplification is to assume that any temperature change which occurs dueto either evaporation or condensation does so at a constant area. Thisimplies that these changes are occurring almost instantaneously in thecase of the condensation. Under these conditions, the effect of heatingcan be determined from the Rayleigh equations where each property isrelated to its value under choked conditions. These equations are:

$\begin{matrix}{{{Pressure}\text{:}\mspace{14mu}\frac{p}{p^{*}}} = \frac{\gamma + 1}{1 + {\gamma\; M^{2}}}} & {{Equation}\mspace{14mu} 7} \\{{{Density}\text{:}\mspace{14mu}\frac{\rho}{\rho^{*}}} = \frac{1 + {\gamma\; M^{2}}}{\left( {\gamma + 1} \right)M^{2}}} & {{Equation}\mspace{14mu} 8} \\{{{Temperature}\text{:}\mspace{14mu}\frac{T}{T^{*}}} = \frac{\left( {\gamma + 1} \right)^{2}M^{2}}{\left( {1 + {\gamma\; M^{2}}} \right)^{2}}} & {{Equation}\mspace{14mu} 9}\end{matrix}$

The effect of a temperature change can then be related to the Machnumber and thus used to calculate the changes in the pressure anddensity of the gas.

One of the principle problems involved in designing the turbineapparatus of the present invention is that of the stability of the flow.One way in which the stability can be compromised is when the flow inthe section between the two hills (the central section) becomessubsonic. If this occurs then the result will be a high pressure regionon the forward facing section of the second hill. This will increase thedrag of the internal structure and reduce the potential thrust of thedevice.

FIG. 8 shows contours of Mach number in a stable scenario withsupersonic flow throughout the central section. Conversely, FIG. 9 showscontours of Mach number in an unstable scenario with subsonic flowthrough the central section.

When considering how this section turns air flow subsonic it is usefulto compare the central section to a similar case which has been wellstudied, being that of a rocket engine nozzle.

FIG. 10 is a graph showing pressure variation through a nozzle fordifferent exit pressures adapted from (Courant & Friedrichs, 1999). FIG.10 illustrates the relationship between the chamber pressure and thepressure along a nozzle for different exit pressures in a rocket engine.If the pressure on the exit is close to the pressure in the chamber (P₁)the result will be a flow which is subsonic throughout. If the pressureon the exit then decreases to a much lower value (P₃) then the flow willbe supersonic throughout. Problems arise when the exit pressure lies ata value between these two points. One of the phenomena which can occurat an exit pressure in this area is a normal shock at a point along thelength nozzle which results in an increase in pressure during theexpansion.

When airflow in the central section of the airfoil turns subsonic it isgenerally this type of phenomena which is observed. The flow issupersonic down the first hill formation of the airfoil but at somepoint down this hill a normal shock occurs resulting in subsonic flow.In FIG. 9 the shock can be seen at the end of the first hill as a rapiddecrease in the Mach number and change in the contours. The keyparameter in stopping this then is the pressure at the ‘exit’ to thefirst hill. For supersonic conditions to be maintained this pressuremust not be too high. The ‘exit’ pressure considered is the increase inpressure as the flow slows to go over the second hill formation. If thissecond hill formation is too high, the result will be the subsonic flowobserved. The minimum throat of this hill can be calculated by using aset methodology.

Calculation methodology for the throat of second hill is as follows:

-   1) If we consider the inlet conditions at a given Mach number, the    stagnation pressure can be calculated using Equation 2.-   2) Knowing the desired Mach number at the base of the hill, the area    at the base of the first hill can be calculated from Equation 4.-   3) The next stage is to assume a normal shock at the base of the    hill and calculate the resulting Mach number.-   4) From the post-shock Mach number and the area at the base of the    hill, the Mach number at the choke conditions can be calculated.-   5) In order to provide an operating margin, the area at a Mach    number of 1.1 is then calculated from the choke conditions.

This area at a Mach number of 1.1 then represents the minimum height ofthe throat at the second hill. For throats larger than this, the flowwill be supersonic throughout the system. If the throat is smaller thanthis, the central section will break down into subsonic flow. Thisprovides one parameter of the turbine in that if the entry Mach number,the throat height at the first hill and the Mach number are known thenthe height of the second hill can be calculated.

One of the conditions which can hamper operation of the turbine is theoccurrence of condensation within the central section of the airfoil,which is understood to be the interface between the first and secondhill formations. The principle reason for this is that if a netcondensation occurs in this area, the evaporation necessary to power thedevice will not occur if sufficient quantities. If the partial pressureof the vapour rises above the saturation pressure of the water at agiven temperature then condensation will start to occur. To preventthis, the partial pressure of the vapour must remain at less than thesaturation pressure.

There are two methods by which the calculation can proceed. Each methodhas its strengths and weaknesses.

The first method involves the similarity laws presented in G. Schnerr'spaper (Schnerr, 1989) in which the Mach number where condensation occursis related to the relative stagnation humidity by the relationship

$\begin{matrix}{{\Phi_{0}^{a} = \frac{\frac{\gamma + 1}{2}}{1 + {\frac{\gamma - 1}{2}M_{c}^{2}}}}{where}{a = {\alpha\left\lbrack {\frac{\gamma + 1}{2\left( {\gamma - 1} \right)}\left( {- \frac{d\left( \frac{T}{T_{01}} \right)}{d\left( \frac{x}{y^{*}} \right)}} \right)^{*}} \right\rbrack}^{\beta}}} & {{Equation}\mspace{14mu} 10}\end{matrix}$and α=0.208 and β=0.59

With the onset Mach number of condensation determined for the givenrelative humidity the maximum Mach in the central section can be chosensuch that it is less that the condensation onset Mach number. From thechosen Mach number, the maximum depth of the device can then becalculated from Equation 4. Note that when cooling is considered here,the mach after the cooling should be considered here for thecondensation onset and the resulting upstream Mach number calculatedbefore obtaining the area. The advantage of this method is that itrepresents a simpler method of calculating the condensation onset,however the variables α and β are only constant for particular familiesof nozzle.

An alternative way is to calculate the onset Mach number from the vapourpressure. It is known that as the Mach number increases, the pressuretemperature and density decrease. From the density of the air and vapourthe molecular volumes of each can be calculated. From these themolecular fraction of the vapour can then also be determined

The partial pressure is the product of the molecular fraction and thestatic pressure. If this partial pressure is greater than the saturatedpressure of the vapour at a given point then condensation will occur.These values can be calculated for each Mach number and the onset Machnumber determined by where the partial pressure and the saturationpressure are equal. From this the area can then be calculated as withthe previous case.

The advantage of this method is that it can be calculated irrespectiveof the shape, however the calculations do not take account of anycurvature which might alter the behaviour of the condensation onset.

From the above calculations a method has been established forcalculating the geometry of the airfoil. FIG. 11 shows the geometry ofthe airfoil design for a ducted scenario when one side holds thefeatures of the hill formations whilst the other side is a flat surface.In this case the entire design can be related back to the throatdiameter, y*.

Knowing y* and the inlet Mach number, calculation of yin can beperformed using Equation 4. From the humidity conditions the depthY_(dip) and the Mach number in the central section can be calculatedfrom either the similarity laws of the vapour pressure. With the Machnumber, after any cooling, and the area Y_(dip) the height of the secondthroat y²* can then be calculated. The exit condition y_(out) then mustbe great enough to ensure that condensation occurs within the section asrequired.

From the design parameters identified previously, a set of operatingconditions for the turbine can be established. In this case, thecondensation onset Mach number is first calculated. If this number isbelow 1 then condensation will begin in the transonic regime.

This means that the condensation will start before the flow passes overthe first hill. This will effectively prevent the turbine fromoperating.

If the condensation onset Mach number is greater than one then,considering the vapour content of the air the temperature increase canalso be calculated. The temperature increase will result in a decreasein Mach number as per the Rayleigh equations. If the Mach numberfollowing the condensation is less than 1 then the flow will be subsonicfrom the point. If the Mach number is between 1 and 1.12 the flow willbe supersonic and an expansion of the area will increase the Mach numbertowards 1.12. Once this point is reached, a normal shock can result inan exit Mach number of 0.9 which matches the entry Mach number. Above aMach number of 1.12 any shock would result in a Mach number lower than0.9 and so some form of variable geometry nozzle would be required onthe exit in order to prevent the normal shock from presenting a problem.

FIG. 12 is a table showing the post-condensation Mach number withvarying temperature and humidity for 10K of cooling. In this table theregion indicated by the arrow B indicates where condensation would occurahead of the first hill, the region indicated by the arrow C showssubsonic Mach numbers after condensation, the region indicated by thearrow D shows where the Mach number is less than 1.12 and the regionindicated by the arrow E shows where the Mach number is above 1.12.

One of the considerations which must be noted with this table is thatfor many of these cases the resulting difference in height between thedip and the second hill is low enough that the second hill may beswamped by the boundary layer developing on the descent from the firsthill. A table of the dip depth with varying temperature and humidity for10K of cooling is shown in FIG. 13.

This can result in a cushioning effect where the flow becomes obliviousto the existence of the dip and a shear layer extends between the peaksof the two hills. In these cases, the Mach number will not increase asrequired and so would disrupt the flow. Care must be taken to ensurethat this increase in height is sufficient that it will be higher thanthe boundary layer.

The calculation of the thrust of the turbine apparatus of the presentinvention is carried out using a CFD analysis of one of the turbineswhich shows potential. The selected turbine represents the case wheretemperature is 30° C. and the relative humidity is 5%. This turbine tieswithin the operating envelope of the device and displays a sufficientdifference in height between the dip of the central section and thesecond throat to ensure that the boundary layer should not interferewith the flow. For this case in order to avoid condensation thecalculated critical geometry details are provided in FIG. 14.

The geometry constructed was 0.5 cm thick and the initial boundaryconditions applied for this simulation are:

-   -   Inlet static pressure=101325 Pa    -   Inlet stagnation temperature=352K    -   Air mass flow=0.092 kg/s (18.4 kg/ms)    -   Vapour mass flow=0.000118602 kg/s (0.02372 kg/ms)    -   Outlet static pressure=20000 Pa

Values in brackets are the mass flow rates per metre width of thedevice. The simulation was run with the Spairt-Allmaras turbulencemodel. The solution was initialised an estimate of the flow parameters.These were deliberate underestimates in order to ensure the stability ofthe convergence. The following settings were used in the initialisation:

-   -   Static pressure=101325 Pa    -   x velocity=283 m/s    -   Temperature=303K

In order for the simulation to proceed in a stable manner the flow wasfirstly calculated assuming zero evaporation and zero condensation untilconvergence of the results was reached. At this point evaporation wasthen added to a zone at the base of the first hill using a negativeenergy source. The simulation was then run again until convergence wasestablished. At this point condensation was added as an energy source ata point suggested by the difference between the partial pressure and thesaturation pressure. Again, the simulation was run until convergence wasreached. The final stage involved increasing the output pressure from20000 Pa to 100800 Pa. This moved the exit towards atmosphericconditions and moved the exit shock to occur just after the condensationin order to accurately model the behaviour on the exit from the turbine.

For a humidity of 5% at 303K the water content of the air is 1.25 g/kg.The evaporation energy extracted was equivalent to a 16K decrease intemperature or an evaporation of 2.22 g/kg whereas the energy sourceused for the condensation was equivalent to a 6.98K increase intemperature or a condensation of 3.47 g/kg.

FIG. 15 is a graph showing the contours of Mach number beforeevaporation is initiated, FIG. 16 is a graph showing the contours ofMach number after evaporation, showing the region where evaporationoccurs, FIG. 17 is a graph showing the contours of Mach number aftercondensation, showing the region where condensation occurs, and FIG. 18is a graph showing the contours of Mach number after exit pressure israised to atmospheric showing a shockwave after the condensation.

Once this process was completed, the resulting thrust could beestablished from a report of the forces over the wall surface. Thisreport was carried out for the working area of the turbine which wasdefined as the interior area between the inlet and the termination shockjust after the condensation. This produced a net thrust in the workingarea of 546N per metre of width of the turbine. This thrust includesdrag effects within the working section of the turbine, but not exteriordrag effects due to the rotor system ducting, the exit geometry or thedifference in height between inlet and outlet. A variable geometrynozzle can then be employed to decrease the area and accelerate the flowback towards 314 m/s alternatively, the exit depth could be decreased toprevent the subsonic diffusion of the velocity. Both of these optionswould decrease the ram drag of the device, whilst also decreasing thethrust produced and thus a balance would have to be obtained.

In order to achieve a positive overall thrust the device must producemore internal thrust than it creates in external drag. A usefulparameter to consider here is the drag coefficient. This is calculatedfrom the equation

$\begin{matrix}{C_{D} = \frac{D}{\frac{1}{2}\rho\; V^{2}A}} & {{Equation}\mspace{14mu} 11}\end{matrix}$where D is the drag on the rotor system and A is the area of the rotors.Assuming a three rotor system with a diameter of 1 m and a chord of 5 cmthis produces an area of 0.075 m². The velocity used in this calculationis the average velocity which will be half the tip velocity.

Then for a rotor with a tip depth of 33 cm, and a therefore a thrust of182N, and normal air density this means that the drag coefficient mustbe less than 0.14 in order for the system to produce a positive thrust.If the drag coefficient of the system can be designed down to a value of0.04, which is common for a streamlined body, then this produces a dragof 50N. Along with bearing losses this gives a total drag of 55.1N. Fora rotor with a tip depth of 33 cm this means that 30% of the availablepower should be set against the initial power gain.

For a moving object, power is equal to the product of the force and thevelocity. For a turbine which is spinning with a tip velocity of 314 m/sthis means that the total power produced on the working area of thedevice is 171 kW/rn (this will further reduce internally to 155 kw whenvariable nozzle costs are included). This is the work being produced bythe evaporation/condensation cycle. The immediate losses reduce thisexternally to 133 kw/rn.

This work shows that, under specific conditions, the turbine will showan increase in the thrust due to the effects of the energy release fromthe condensation. If the external rotors/pumping can be designed in sucha way as to maintain the losses to below the thrust of the device thenit will produce a net thrust. Given the speed at which the devicerotates, even a small increase in the thrust would produce a largeincrease in the available power.

During this work it has been assumed that the device will be an internalstructure. This implies the existence of an exterior surface. Theaerodynamic design of such a structure would be crucial to the operatingof the turbine as it would have fundamental implications for the drag ofthe device, and hence the net power production.

The operating conditions of the device are quite sensitive. For a givenhumidity then higher temperatures result in more available water in theair to be condensed. This would mean the available power would begreater. As FIG. 13 shows, for any given temperature the depth to whichthe central section can drop is greater for higher temperatures as well.This would produce a device which is easier to manufacture. Thesedesigns are also less vulnerable to the effects of the boundary layersas the difference in height between the central section and the secondhill will be greater as well.

For a given temperature an increase in the humidity would result in anincrease of available power, but would also cause the condensation tooccur earlier since the partial pressure will be higher. This means thatthe depth to which the central section would drop would decrease and thedevice would be more vulnerable to the boundary layer effectsdestabilising the flow. By reducing the amount of coolant used, thetemperature drop will be decreased and as a consequence the saturationpressure would be increased. By correctly balancing the amount ofcoolant used to the humidity the operating range of a given physicaldesign could be extended.

For the purposes of this analysis the device is designed to operate inconditions where the atmospheric temperature is high and relativehumidity levels are low. An increase in the humidity can be somewhatcountered by decreasing the cooling used in order to maintain the flowstability. These conditions would suggest that the device is more easilyanalysed in warm, arid climate conditions. This abundance of humiditycould be managed by using a ‘dry’ coolant and allowing extracondensation to occur on the rear slope of the first hill. In aridplaces, the condensation produced as a by-product of the device wouldalso be quite valuable and so this increases the value of the device asa whole.

It is worth noting that for a given set of conditions, the criticalgeometry can be found from a purely mathematical method. In order toinvestigate the effects of boundary layer and to evaluate the thrust,CFD presents the best available method.

The combination of these approaches has shown that there exists anoperational envelope for the turbine. This range is described by acombination of the temperature, relative humidity and amount of coolingemployed in the device. If for a fixed temperature and cooling, if thehumidity is too high then condensation will occur before the flowbecomes choked disrupting the entire process. Inside the turbine itself,these factors can influence the design of the device, but varying theamount of cooling can compensate for some variations in the otherfactors. Using a ‘dry’ coolant such as nitrogen instead of water willextend the operating range as such a coolant could be evaporated whenwater is condensing between the hills.

When the device is operated within its envelope and the drag on theexternal features are minimised then the device will generate a positivethrust. At the speeds at which the device rotates, even small increasesin the thrust can create a sizable amount of power.

The design produced from the CFD calculations is a three rotor systemwith a diameter of 1 m. The tips have a depth of 33 cm and the systemrotates at 6000 rpm. It is designed to operate in desert conditions of5% relative humidity and 30° C. This device will produce 133 kW of powerand produces 81 litres per hour (1944 litres per day) of water. Sincethe ‘fuel’ for this device is humid fresh air it produces no CO₂ and hasno supply costs. Finally, the device can be turned on and off asrequired as long there is sufficient humidity in the air.

Various embodiments disclosed herein have the same common source ofenergy, however requirements for power, water, heat, cryogenics, spotcooling/heating or pumping will vary exact materials and scalespecifications. Along with this the general environment in which themachine must operate will also dictate material and scale. Those personsskilled in the art will recognise the common requirement of smooth andrigid surfaces to operate effectively at high subsonic speeds.

These designs are resistant to high speed winds and have no obviousvulnerabilities to earthquake, tsunami and other natural disasters.Indeed localised significant fire can be managed with copious supply ofwater and pumping ability drawn directly from the air.

The present invention does have limitations in how cold and dry theambient air can be for viable energy extraction. Typically more than agram of water vapour per kilogram of air will be required. This meansthat temperatures will have to be above −20° C. If there is even apossibility of a vital utility failing, an alternative method needs tobe relied on. Hence where this design evaporates liquid it will normallybe water but can be a hydrocarbon-methanol say—which has a comparablelatent heat of evaporation. Where this design adds heat due to thelatent heat of condensation it can be the chemical heat of combustion ofsaid hydrocarbon air mixture.

This will of course dictate material, pumping and spray specificationsand in addition an ignition system. The possibility of this requirementmay dictate features of design even if they are never used in practice.However this means that no backup plant will be required when specifyingthese utilities. Burning Hydrocarbons under these circumstances has azero impact on the environment as the fuels would be synthesised withthe excess power available in warmer more moist periods. IfCO₂+H₂O—>Hydrocarbons+O₂ are synthesised using excess power whenavailable, then when it is burned Hydrocarbons+O₂->CO₂+H₂O and returnssome of the power originally invested. Note the net production of CO₂ iszero.

Thus combining one or more of the foregoing techniques for powerproduction, water collection, direct electric power production,cryogenic/superconducting environment maintenance, pumping, heating orcooling, the specification can be detailed. The resulting flexibilityprovides designers with a wide choice for configuring an engine for thepurpose(s) required.

Further Embodiments

Further embodiments of the present invention include:

1. A turbine airfoil substantially as herein described with reference toand/or as shown in the accompanying drawings.

2. A turbine apparatus substantially as herein described with referenceto and/or as shown in the accompanying drawings.

Aspects of the present invention have been described by way of exampleonly and it should be appreciate that additions and/or modifications maybe made thereto without departing from the scope thereof as defined inthe appended claims.

The invention claimed is:
 1. A turbine airfoil for relative movement inan ambient fluid, comprising: a main spar having a cross-sectional shapeof an airfoil with a top side wall and a bottom side wall, a leadingedge, a trailing edge, and a camber line extending from said leadingedge to said trailing edge, wherein movement of said airfoil relative tosaid ambient fluid causes said ambient fluid to flow over said main sparin a downstream direction from said leading edge to said trailing edge,and discharge means operable to selectively discharge an evaporativefluid and a condensing fluid into said ambient fluid; wherein said mainspar has a side wall extending from said leading edge to said trailingedge, said side wall having a first hill formation and a second hillformation, wherein both said first hill formation and said second hillformation include a first region of progressively increasing distancefrom said camber line, a second region of progressively decreasingdistance from said camber line, and a crest at an interface between saidfirst region and said second region, wherein said first region of saidfirst hill formation is operable to interact with said ambient fluid toaccelerate said ambient fluid from a high subsonic relative speed to asonic relative speed over said crest of said first hill formation and asupersonic speed after said crest of said first hill formation; whereinsaid discharge means is operable to discharge said evaporative fluid toevaporate into said ambient fluid before condensation onset in saidsecond region of said first hill formation, said second region of saidfirst hill formation interacting with said ambient fluid to acceleratesaid ambient fluid from a supersonic relative speed to a highersupersonic relative speed; said first region of said second hillformation being operable to interact with said ambient fluid todecelerate and maintain said ambient fluid at said supersonic relativespeed over said crest of said second hill formation, and wherein saiddischarge means is further operable to discharge said condensing fluidto nucleate condensation shock in said ambient fluid flowing over saidsecond region of said second hill formation to decelerate said ambientfluid from said supersonic relative speed to said subsonic relativespeed and generate a pressure on said side wall to impart thrust on saidairfoil.
 2. A turbine airfoil as claimed in claim 1, in which saidevaporating fluid is discharged before said condensation shock in saidambient fluid flowing over said first hill formation.
 3. A turbineairfoil as claimed in claim 1, wherein said condensing fluid isdischarged before said condensation shock occurs in said ambient fluidflowing over said second hill formation.
 4. A turbine airfoil as claimedin claim 1, wherein said discharge means comprises at least one nozzle,and said evaporative fluid and said condensing fluid are conveyed from asupply to said at least one nozzle via an arrangement of conduits.
 5. Aturbine airfoil as claimed in claim 1, wherein said main spar comprisesa hollow cavity containing a working fluid, whereby said cavity isdivided into a plurality of interconnected chambers.
 6. A turbineairfoil as claimed in claim 5, wherein said working fluid flowing intoeach of said plurality of interconnected chambers is controlled toselectively adjust pressure and temperature of said working fluid ineach of said plurality of interconnected chambers independently.
 7. Aturbine airfoil as claimed in claim 1, wherein said evaporative fluid isselected from a group consisting of: water, liquid nitrogen and ahydrocarbon.
 8. A turbine airfoil as claimed in claim 7, wherein saidevaporative fluid comprises fluid particles that have a diameteroperable to evaporate in said ambient fluid.
 9. A turbine airfoil asclaimed in claim 1, wherein said condensing fluid comprises fluidparticles that are cooled and statically charged.
 10. A turbine airfoilas claimed in claim 1, wherein said ambient fluid is air.